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Differentiating Math Instruction

Differentiating Math Instruction
Strategies That Work for K-8 Classrooms

Second Edition
Edited by:

152 pages | Corwin
'Bender presents a variety of ways to differentiate instruction and foster dynamic learning' — Scott Currier, Mathematics Teacher, Belmont High School, NH

'This is one of those rare opportunities when a teacher can read a book and become inspired to take ideas immediately back to the classroom' — Amanda P. McKee, Math Instructor, Florence £5 School District, Johnsonville, SC

Differentiate math instruction with practices that boost mastery for all students!

Experienced teachers understand and appreciate that all students learn and process information according to their individual styles, abilities, and preferences. William N. Bender provides teachers with a wealth of critical strategies and teaching ideas for differentiating instruction to leverage each learner's unique abilities and raise student achievement in math.

With updated information and recommendations based on the 2008 National Mathematics Advisory Panel report, this new edition of Differentiating Math Instruction includes research on the value of brain-compatible teaching and creative ways to get students visualizing, vocalizing, and moving during math to make instruction more meaningful, motivational, and successful. New and seasoned teachers alike will be able to quickly adapt the techniques to suit their specific classrooms, with key features including:

- Strategies for use within a Response to Intervention framework

- At-a-glance lists of "Top Ten Tactics" for successful implementation

- "Web Site Reviews" that outline additional online resources

- Concrete strategies to tap into multiple intelligences

- A facilitator's guide for staff developers to train teachers in differentiating math instruction

Engage every student in a deep conceptual understanding of mathematics with this key resource aimed at revitalizing mathematics instruction in the elementary and middle school classroom.

Preface: How to Use This Book
About the Author
1. The Mathematical Brain and High-Impact Teaching
Teaching Mathematics Through Differentiating Instruction

The Mathematical Brain

Brains as Prioritizing Filters

Number Sense

Multiple Intelligences: Avenues for Learning Math

Summary of Brain Research

Instructional Phases for Developing Math Skills

Teaching Strategy: Mathematical Games to Develop Number Sense

SHEMR: A Tool for High-Impact Learning in Mathematics Evaluating One’s Own Instructional Planning

What’s Next?

2. Differentiated Instruction and Response to Intervention in Mathematics
Differentiation and Response to Intervention: Refocusing Math Instruction

Teaching Phases in the Direct Instruction Lesson

Problems With Direct Instruction in a Large Class

Teaching Strategy: The Guess, Assess, and Tear Out Tactic

A Differentiated Instruction Lesson Example

Teaching Strategy: Using Guess, Assess, and Tear Out! Moving From Direct Instruction to Differentiated Instruction in Math

The Omega Group

The Mainline Instruction Group

The Beta Group

Is Further Differentiation Needed?

Anything Wrong With This Scenario? Enhancing the Differentiated Instruction Model

Guidelines for Differentiated Lesson Planning

Results of Differentiated Lessons

A Differentiated Instruction Overview: What It Is and What It Isn’t

Response to Intervention in Mathematics

Case Study: A RTI for Number Sense and Early Math Skill

What’s Next?

3. Differentiating for Primary and Elementary Math
Research on Math Readiness

Steps in Developing Early Math Skills

Teaching Strategy: A Concrete, Semi-Concrete, Abstract Learning Tactic

Using CSA in the Classroom

CSA in the Higher Grades

Summary: CSA Tactic

Teaching Strategy: The Errorless Learning Procedures

Summary: Errorless Learning

Teaching Strategy: Classwide Peer Tutoring for Differentiating in the Math Class

What’s Next?

4. Differentiating for Deep Conceptual Understanding
High-Impact Teaching for Operations in Math

The Debate on Calculators in Elementary Mathematics

Constructivist Theory and Understanding of Mathematics

Using Cognitive Guided Visualization

Scaffolded Instruction in Math

Debate on What a Scaffold Is

Graphic Representations of Word Problem Schemas

Using a Representational Strategy

Teaching Expanded Notation and Partialing

Process Mnemonics Strategies to Teach Computation

Research Support

What’s Next?

5. Differentiating With Learning Strategies
The Brain Research Basis for Metacognitive Theory and Tactics

Learning Strategies for Word Problems

The Schema-Based Math Strategy

Differentiated Tear Out Activities for Story Problem Schemas

What’s Next?

6. Differentiating in the Middle Grades
Working Toward Higher-Order Thinking

Teaching Strategy: Anchored Instruction

Teaching Games in Higher Grades

The PASS Strategy

Moving On Up! Math Instruction Guidelines for Secondary Learners


"This is one of those rare opportunities when a teacher can read a book and become inspired to take ideas immediately back to the classroom and use them. This book provides an effective plan to help teachers reach all their students using proven and researched strategies. It guides today's classroom teacher who is struggling to help a diverse student population become successful."

Amanda P. McKee, Math Instructor
Florence #5 School District, Johnsonville, SC

"This book provides refreshing strategies that work in the classroom. Bender has presented us with a variety of ways to differentiate instruction and foster dynamic learning. This work is a gift to individuals who are constantly looking for ways to improve their practice."

Scott Currier, Mathematics Teacher
Belmont High School, NH

"William Bender's book should be a necessity for the bookshelf of anyone who teaches math. It speaks to the educator who may be struggling to reach all math learners in his or her classroom. It also reaches the math coach who is inspired by Bender's work and who wishes to spread this wealth of knowledge to other educators. There is truly something for everybody."

Carl Ameen Jr., Principal
Allendale Elementary School, Pittsfield, MA

"A fantastic resource for first-year teachers and veterans alike. Bender’s research base combines with creativity and multiple approaches to yield a great reference that teachers can use over and over again."

Randy Wormald, Mathematics Teacher, Belmont High School, NH
Former Math Teacher, Londonderry Junior High School

"The structure of the book invites teachers to enter into the text based on their questions—by design, a differentiated resource! The book is an excellent choice for a study group to begin the conversation on differentiation in mathematics. The inclusion of a facilitator's guide provides further questions and activities for deepening teachers' understanding of differentiation in mathematics."

Thelma A. Davis, Principal
Clark County School District, Las Vegas, NV
Key features
New and seasoned educators alike will be quick to put the following key features to use in their classrooms:

  • "Ideas From Teachers" sections that highlight actual examples of the differentiation process in action
  • At-a-glance lists of "Top Ten Tactics" for successful implementation in K-8 classrooms
  • "Web Site Reviews" that outline additional online resources for effective mathematics instruction
  • Concrete strategies to tap multiple intelligences
Research on the value of brain-compatible teaching is combined with teacher-generated tips, including creative ways to get students visualizing, vocalizing, and moving during math-to make instruction more meaningful, motivational, and successful.

While the new edition remains structurally similar to the previous edition, the author made many revisions throughout the text. He added new references to recent research on learning and mathematics, including statistics on mathematics achievement and new studies about the brain. In addition, the author updated the material by explaining how differentiated math instruction correlates with the recommendations made by the National Mathematics Advisory Panel in 2006. The book includes a list of selected recommendations from the panel's report. Several new teaching strategies and examples have been included, as well as sections about response to intervention. In these sections the author includes explanations of RTI, case studies of RTI in mathematics, and figures to illustrate the intervention process.

William N. Bender

Learn more about William Bender's PD offeringsConsulting Description: Differentiated InstructionConsulting Description: MathConsulting Description: Project-Based LearningConsulting Description: RTIConsulting Description: Technology  William N. Bender began his career by teaching eighth- and ninth-grade students in the public schools. He worked in higher education for 28 years and published over 60 research articles and 24 books in education. He specializes in instructional strategies for all students and is recognized as a national leader on instructional tactics, response to intervention, and differentiated instruction. Dr.... More About Author